Community translation (French to English) of A. Grothendieck and J. Dieudonné's Éléments de géométrie algébrique. Désolé, Grothendieck.

For discussion regarding this project, visit #ega:matrix.org!

To compile, make book, make pdfs, or make all.

The PDFs are automatically generated whenever any changes are made, and you can always find the latest version on the releases page.

Summary:

• EGA I preliminaries
• EGA I
• EGA II
• EGA III preliminaries
• EGA III
• EGA IV preliminaries
• EGA IV

Details: Here is the current status of the translation, along with who is currently working on/has worked on which sections. (Page counts and percentages are usually just rough estimates).

1. Rings of fractions (@ryankeleti)
2. Irreducible spaces. Noetherian spaces (@ryankeleti)
3. Supplement on sheaves (@ryankeleti)
4. Ringed spaces (@ryankeleti)
5. Quasi-coherent sheaves and coherent sheaves (@ryankeleti)
6. Flatness (@ryankeleti)
7. Adic rings (@ryankeleti)

• 8. Representable functors (@ryankeleti)
• 9. Constructible sets (@ryankeleti)
• 10. Supplement on flat modules (@thosgood)
• 11. Supplement on homological algebra (@ryankeleti, @wayneyang108)
• 12. Supplement on sheaf cohomology (~25 pages)
• 13. Projective limits in homological algebra (~10 pages)

• (14-ε). Summary (@thosgood)
• 14. Combinatorial dimension of a topological space (@thosgood)
• 15. M-regular and F-regular sequences (~10 pages)
• 16. Dimension and depth of Noetherian local rings (~15 pages)
• 17. Regular rings (~15 pages)
• 18. Supplement on extensions of algebras (~20 pages)
• 19. Formally smooth algebras and Cohen rings (~45 pages)
• 20. Derivations and differentials (~35 pages)
• 21. Differentials in rings of characteristic p (~30 pages)
• 22. Differential criteria for smoothness and regularity (~30 pages)
• 23. Japanese rings (~5 pages)

0. Summary
1. Affine schemes (@ryankeleti)
2. Preschemes and their morphisms (@thosgood)
3. Products of preschemes (@thosgood, @ryankeleti)
4. Subpreschemes and immersions (@ryankeleti)
5. Reduced preschemes; separation condition (@thosgood)
6. Finiteness conditions (@thosgood)
7. Rational maps (@thosgood)
8. Chevalley schemes (@thosgood)
9. Supplement on quasi-coherent sheaves (@thosgood)
10. Formal schemes (@thosgood, @ryankeleti)

• 0. Summary (@ryankeleti / proofread by @thosgood)
• 1. Affine morphisms (@ryankeleti)
• 2. Homogeneous prime spectra (@thosgood)
• 3. Homogeneous prime spectrum of a sheaf of graded algebras (@thosgood)
• 4. Projective bundles; Ample sheaves (@thosgood)
• 5. Quasi-affine morphisms; quasi-projective morphisms; proper morphisms; projective morphisms (@thosgood)
• 6. Integral morphisms and finite morphisms (@thosgood)
• 7. Valuative criteria (@thosgood)
• 8. Blowup schemes; based cones; projective closure (@thosgood)
• Errata and addenda (list 1) (@thosgood)

• 0. Summary (@thosgood / proofread by @thosgood)
• 1. Cohomology of affine schemes (@ryankeleti)
• 2. Cohomological study of projective morphisms (~15 pages) (@thosgood)
• 3. Finiteness theorem for proper morphisms (@ryankeleti)
• 4. The fundamental theorem of proper morphisms. Applications (~30 pages) (@calebji0)
• 5. An existence theorem for coherent algebraic sheaves (~10 pages)
• 6. Local and global Tor functors; Künneth formula (~40 pages)
• 7. Base change for homological functors of sheaves of modules (~30 pages)
• 8. The duality theorem for projective bundles
• 9. Relative cohomology and local cohomology; local duality
• 10. Relations between projective cohomology and local cohomology. Formal completion technique along a divisor
• 11. Global and local Picard groups
• Errata and addenda (list 2)

• 0. Summary (@thosgood)
• 1. Relative finiteness conditions. Constructible sets of preschemes (~30 pages)
• 2. Base change and flatness (~30 pages)
• 3. Associated prime cycles and primary decomposition (~15 pages)
• 4. Change of base field for algebraic preschemes (~35 pages)
• 5. Dimension, depth, and regularity of locally Noetherian preschemes (~50 pages)
• 6. Flat morphisms of locally Noetherian preschemes (~50 pages)
• 7. Relations between a local Noetherian ring and its completion. Excellent rings (~40 pages)
• 8. Projective limits of preschemes (~50 pages)
• 9. Constructible properties (~40 pages)
• 10. Jacobson preschemes (~20 pages)
• 11. Topological properties of finitely presented flat morphisms. Flatness criteria (~60 pages)
• 12. Fibres of finitely presented flat morphisms (~15 pages)
• 13. Equidimensional morphisms (~15 pages)
• 14. Universally open morphisms (~25 pages)
• 15. Fibres of a universally open morphism (~25 pages)
• 16. Differential invariants. Differentially smooth morphisms (@solov-t) (~50 pages)
• 17. Smooth morphisms, unramified morphisms, and étale morphisms (@tholzschuh) (~55 pages)
• 18. Supplement on étale morphisms. Henselian local rings and strictly local rings (~75 pages)
• 19. Regular immersions and normal flatness (~40 pages)
• 20. Meromorphic functions and pseudo-morphisms (~30 pages)
• 21. Divisors (~75 pages)
• Errata and addenda (list 3)

• check errata in EGA III and onwards
• more consistent use of Proposition/Theorem/Definition/whatever in front of \srefs
• lists of notation?
• terminology indices?
• hyperref links to equations (e.g. 3.3.9.1)
• check for any \unsure commands in the source
• check that all \hyperref references are found
• when this is finished (?!) should we assign a DOI?
• web version? (work in progress!)
• more detailed style guidelines? (e.g. language, sentence construction, etc.)
• link (M), (G), (T) references